When evolving rigid bodies using forces you integrate the force applied along the COM and integrating the torque using eulers equations of motion.
I am confused on how you approach this problem using impulses instead. You can update the linear velocity with the impulse in the same way, but how do you update the rotational state of the object using impulses instead of forces?
The difference between viewing the interaction as impulse vs a force is that a force needs to be applied over a certain amount of time to generate a momentum. If you know the momentum that will be transferred the object, there is no need to integrate the forces, the value of the momentum is already the result of the integral. This applies both for linear momentum using forces and for angular momentum (using torques).
Using the Newton's Cradle as classical example for the translatorial case: If you release one of the outer steel balls from a given angular position, you can calculate the speed the ball will have at the moment of impact, and hence you can calculate the momentum that this ball has at that moment. From here you can continue calculating momentum balances (and energy balances in case of elastic impact) If you were to use forces and dynamics, that becomes a lot harder, because you will need to know the elastic dynamic properties of said steel ball (the force-deformation curve for elastic deformation of a steel ball will be highly non-linear)
Note that impulses are only a valid approximation for when the interaction times are short compared to the system you are analyzing.
